The agrarian polytope of two-generator one-relator groups

Henneke, Fabian; Kielak, Dawid

doi:10.1112/jlms.12334

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学術論文

The agrarian polytope of two-generator one-relator groups

MPS-Authors

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Henneke, Fabian
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1112/jlms.12334
(出版社版)

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フルテキスト (公開)

arXiv:1912.04650.pdf
(プレプリント), 621KB

Henneke-Kielak_The agrarian polytope of two-generator one-relator groups_2020.pdf
(出版社版), 356KB

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引用

Henneke, F., & Kielak, D. (2020). The agrarian polytope of two-generator one-relator groups. Journal of the London Mathematical Society, 102(2), 722-748. doi:10.1112/jlms.12334.

引用: https://hdl.handle.net/21.11116/0000-0006-9E42-E

要旨

Relying on the theory of agrarian invariants introduced in previous work, we
solve a conjecture of Friedl-Tillmann: we show that the marked polytopes they
constructed for two-generator one-relator groups with nice presentations are
independent of the presentations used. We also show that, when the groups are
additionally torsion-free, the agrarian polytope encodes the splitting
complexity of the group. This generalises theorems of Friedl-Tillmann and
Friedl-Lück-Tillmann.